We show that Kerr beam self-cleaning results from parametric mode mixing instabilities, that generate a number of nonlinearly interacting modes with randomised phases -optical wave turbulence, followed by a direct and inverse cascade towards high mode numbers and condensation into the fundamental mode, respectively. This optical self-organization effect is analogue to wave condensation that is well-known in hydrodynamic 2D turbulence.

We investigate the application of dynamic deep neural networks for nonlinear equalization in long haul transmission systems. Through extensive numerical analysis we identify their optimum dimensions and calculate their computational complexity as a function of system length. Performing comparison with traditional back-propagation based nonlinear compensation of 2 steps-per-span and 2 samples-per-symbol, we demonstrate equivalent mitigation performance at significantly lower computational cost.

A scheme for compensation of nonlinear effects in multichannel data transfer systems based on dynamic neural networks is proposed. An improved quality of optical signal transfer in this scheme in comparison with the signal transfer in a scheme based on a neural network using symbols from only one channel is demonstrated.

Practical implementation of digital signal processing for mitigation of transmission impairments in optical communication systems requires reduction of the complexity of the underlying algorithms. Here, we investigate the application of convolutional neural networks for compensating nonlinear signal distortions in a 3200 km fiber-optic 11x400-Gb/s WDM PDM-16QAM transmission link with a focus on the optimization of the corresponding algorithmic complexity. We propose a design that includes original initialisation of the weights of the layers by a filter predefined through the training a single-layer convolutional neural network. Furthermore, we use an enhanced activation function that takes into account nonlinear interactions between neighbouring symbols. To increase learning efficiency, we apply a layer-wise training scheme followed by joint optimization of all weights applying additional training to all of them together in the large multi-layer network. We examine application of the proposed convolutional neural network for the nonlinearity compensation using only one sample per symbol and evaluate complexity and performance of the proposed technique. Index Terms-Convolutional neural networks. Nonlinearity mitigation in fiber-optic links.

No abstract

It has been recently demonstrated that multimode solitons are unstable objects which evolve, in the range of hundreds of nonlinearity lengths, into stable single-mode solitons carried by the fundamental mode. We show experimentally and by numerical simulations that femtosecond multimode solitons composed by non-degenerate modes have unique properties: when propagating in graded-index fibers, their pulsewidth and energy do not depend on the input pulsewidth, but only on input coupling conditions and linear dispersive properties of the fiber, hence on their wavelength. Because of these properties, spatiotemporal solitons composed by non-degenerate modes with pulsewidths longer than a few hundreds of femtoseconds cannot be generated in graded-index fibers.

We experimentally demonstrate that spatial beam self-cleaning can be highly efficient when obtained with a few-mode excitation in graded-index multimode optical fibers. By using 160 ps long, highly chirped (6 nm bandwidth at -3dB) optical pulses at 1562 nm, we demonstrate a one-decade reduction of the power threshold for spatial beam self-cleaning, with respect to previous experiments using pulses with laser wavelengths at 1030-1064 nm. Self-cleaned beams remain spatio-temporally stable for more than a decade of their peak power variation. The impact of input pulse temporal duration is also studied.

The impact of the fiber Kerr effect on error statistics in the nonlinear (high power) transmission of the OFDM 16-QAM signal over a 2000 km EDFA-based link is examined. We observed and quantified the difference in the error statistics for constellation points located at three power-defined rings. Theoretical analysis of a trade-off between redundancy and error rate reduction using probabilistic coding of three constellation power rings decreasing the symbol-error rate of OFDM 16-QAM signal is presented. Based on this analysis, we propose to mitigate the nonlinear impairments using the adaptive modulation technique applied to the OFDM 16-QAM signal. We demonstrate through numerical modelling the system performance improvement by the adaptive modulation for the large number of OFDM subcarriers (more than 100). We also show that a similar technique can be applied to single carrier transmission.